In most calculus courses, students are taught the theory of Riemann Integration. Although very useful, the Riemann integral has a number of shortcomings that can make it difficult/impossible to work with. In this course, we construct the Lebesgue integral and the measure-theoretic machinery that powers it.

Introduction to Group Theory: As devices for measuring symmetry, groups occupy a central role in several areas of mathematics. This course begins with the definition of a group and finishes with the Sylow Theorems for finite groups and the Fundamental Theorem of Finite Abelian Groups. Emphasis is placed on teaching through examples.